Page 30 - Fisika Terapan for Engineers and Scientists

230 CHAPTER 7 Work and Energy

47. A 1300-kg communication satellite has a speed of 3.1 km/s. 56. What is the kinetic energy and what is the gravitational
What is its kinetic energy? potential energy (relative to the ground) of a goose of mass
48. Suppose you throw a stone straight up so it reaches a maxi- 6.0 kg soaring at 30 km/h at a height of 90 m?
mum height h. At what height does the stone have one-half its 57. Surplus energy from an electric power plant can be temporar-
initial kinetic energy? ily stored as gravitational energy by using this surplus energy
49. The velocity of small bullets can be roughly measured with to pump water from a river into a reservoir at some altitude
ballistic putty. When the bullet strikes a slab of putty, it pene- above the level of the river. If the reservoir is 250 m above the
trates a distance that is roughly proportional to the kinetic level of the river, how much water (in cubic meters) must we
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energy. Suppose that a bullet of velocity 160 m/s penetrates pump in order to store 2.0 10 J?
0.80 cm into the putty and a second, identical bullet fired 58. The track of a cable car on Telegraph Hill in San Francisco
from a more powerful gun penetrates 1.2 cm. What is the rises more than 60 m from its lowest point. Suppose that a car
velocity of the second bullet? is ascending at 13 km/h along the track when it breaks away
50. A particle moving along the x axis is subject to a force from its cable at a height of exactly 60 m. It will then coast up
F ax bx 3 the hill some extra distance, stop, and begin to race down the
x
hill. What speed does the car attain at the lowest point of the
where a and b are constants.
track? Ignore friction.
(a) How much work does this force do as the particle moves
59. In pole vaulting, the jumper achieves great height by converting
from x to x ?
1 2 her kinetic energy of running into gravitational potential energy
(b) If this is the only force acting on the particle, what is the (Fig. 7.32).The pole plays an intermediate role in this process.
change of kinetic energy during this motion? When the jumper leaves the ground, part of her translational
*51. In the “tapping mode” used in atomic-force microscopes, a tip kinetic energy has been converted into kinetic energy of rota-
on a cantilever taps against the atoms of a surface to be studied. tion (with the foot of the pole as the center of rotation) and part
The cantilever acts as a spring of spring constant 2.5 10 2 has been converted into elastic potential energy of deformation
N/m. The tip is initially displaced away from equilibrium by of the pole. When the jumper reaches her highest point, all of
3.0 10 8 m; it accelerates toward the surface, passes through this energy has been converted into gravitational potential
the relaxed spring position, begins to slow down, and strikes energy. Suppose that a jumper runs at a speed of 10 m/s. If the
the surface as the displacement approaches 2.5 10 8 m. What jumper converts all of the corresponding kinetic energy into
kinetic energy does the tip have just before striking the surface? gravitational potential energy, how high will her center of mass
*52. With the brakes fully applied, a 1500-kg automobile deceler- rise? The actual height reached by pole vaulters is 5.7 m (meas-
2
ates at the rate of 8.0 m/s . ured from the ground). Is this consistent with your calculation?
(a) What is the braking force acting on the automobile?
(b) If the initial speed is 90 km/h, what is the stopping distance?
(c) What is the work done by the braking force in bringing
the automobile to a stop from 90 km/h?
(d) What is the change in the kinetic energy of the automobile?
*53. A box of mass 40 kg is initially at rest on a flat floor. The
coefficient of kinetic friction between the box and the floor is
0.60. A woman pushes horizontally against the box with
k
a force of 250 N until the box attains a speed of 2.0 m/s.
(a) What is the change of kinetic energy of the box?
(b) What is the work done by the friction force on the box?
FIGURE 7.32 A pole vaulter.
(c) What is the work done by the woman on the box?
60. Because of brake failure, a bicycle with its rider careens down a
7.4 Gravitational Potential Energy † steep hill 45 m high. If the bicycle starts from rest and there is no
friction, what is the final speed attained at the bottom of the hill?
54. It has been reported that at Cherbourg, France, waves smashing
61. Under suitable conditions, an avalanche can reach extremely
on the coast lifted a boulder of 3200 kg over a 6.0-m wall. What
great speeds because the snow rides down the mountain on a
minimum energy must the waves have given to the boulder?
cushion of trapped air that makes the sliding motion nearly
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55. A 75-kg man walks up the stairs from the first to the third frictionless. Suppose that a mass of 2.0 10 kg of snow
floor of a building, a height of 10 m. How much work does he breaks loose from a mountain and slides down into a valley
do against gravity? Compare your answer with the food energy 500 m below the starting point. What is the speed of the snow
he acquires by eating an apple (see Table 8.1). when it hits the valley? What is its kinetic energy? The explo-
†
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